Suppose that an upward jet of water strikes an unsupported, horizontal plate of mass mp, as shown in Fig. P11.9. The diameter of the turbulent jet is D(z) and its velocity is v(z). The diameter and velocity at the nozzle (z = 0) are D0 and v0, respectively.

(a) As it rises the jet will be slowed by gravity, and as it slows it must widen. Determine D(z) and v(z) in the main part of the jet.

(b) Derive an expression for the net fluid force on the plate. A convenient control volume is shown by the dashed lines. You may assume that the actual thickness of the control volume is much less than H and that the mass of water it contains is negligible.

(c) If m_p = 1 kg and D₀ = 0.1 m, what nozzle velocity v₀ would be needed to suspend the plate at H = 1 m?

Transcribed Image Text:

H Air Po Z mp ↑| V(2) -D(z) Water Figure P11.9 A plate of mass m, suspended at a height H by an upward jet of water.